Next, according to Yong [1]}, Wang–Sun–Yong [2]}, in the one-dimensional case, if instead of the return \(\xi \)  at the terminal time \(T\) , one has an \({\cal F}_T\) -measurable position process \(\psi (\cdot )\)  (not necessarily \(\mathbb {F}\) -adapted), to dynamically measure the risk, it will be more proper to consider the following BSVIE:
\(Y(t)=-\psi (t)+\int _t^Tg(t,s,Z(t,s))ds-\int _t^TZ(t,s)dW(s),\ \ t\in [0,T],\) 
